Many theories of politics assume people with shared interests will form interest groups, but rational choice models suggest this is actually rare for certain types of goods and certain types of group.
| Rival | Non-Rival | |
|---|---|---|
| Excludable | Private goods | Common-pool resources |
| Non-excludable | Club goods | Public Goods |
Utility maximization: given two options, a rational actor will choose the one that maximizes their expected utility.
Completeness: I can compare any pair of options and tell you whether one is better, worse, or equal.
Transitivity: If A > B and B > C then A > C. In other words, I can consistently rank all of my options from best to worst.
Classical models typically assume perfect information: I know everything necessary to quantify the utility of a decision, but this is often relaxed.
A simplified version of an expected utility model for a decision with an uncertain outcome looks like this:
\[ EU(A) = U_{pg} \times P(PG|A) - C \]
\(P(PG|A)\) = The probability of “winning” or “success” given that you did action “A”
\(U_{pg}\) = The utility gained from success
\(C\) = The costs of action A
\(EU(A)\) = the expected Utility from action A
\[ EU(A) = U_{pg} \times P(PG|A) - C \]
The expected utility from not doing action A is:
\[ EU(\neg A) = U_{pg} \times P(PG|\neg A) \]
\(\neg\) = negation symbol. Read as “NOT”
What’s the expected utility for playing the lottery?
\[ EU(A) = U_{pg} \times P(PG|A) - C \]
Payoff for playing:
\(P(PG|A)\) = \(1 \text{ in } 292,201,338\) or \(0.000000003422298\)
\(U_{pg}\) = Initial projected jackpot: \(\$20,000,000\)
\(C\) = The costs of a ticket: \(\$2\)
\(EU(A)\) = \((0.000000003422298\times \$20,000,000) - \$ 2 = -\$1.93\)
What’s the expected utility for NOT playing the lottery?
\[ EU(\neg A) = U_{pg} \times P(PG|\neg A) \]
Payoff for NOT playing:
\(P(PG|\neg A)\) = \(0\)
\(U_{pg}\) = Initial projected jackpot: \(\$20,000,000\)
\(C\) = The costs of not buying a ticket: \(0\)
\(EU(\neg A)\) = \((0\times \$20,000,000) - \$ 0 = \$0\)
\[ EU(A) = U_{pg} \times P(PG|A) - C \]
\[ EU(\neg A) = U_{pg} \times P(PG|\neg A) \]
When does playing the lottery become rational? In other words, when does \(EU(\neg A) < EU(A)\)?
How do intangible goods like “equal rights” or policies like “social welfare” differ from playing a lottery?
\[ EU(A) = U_{pg} \times P(PG|A) - C \]
\[ EU(\neg A) = U_{pg} \times P(PG|\neg A) \] . . .
\(P(PG|\neg A)\) is always zero for the lottery, but I can enjoy the benefits of “rights” without paying.
If \(P(PG|\neg A)\) is close to \(P(PG|A)\) then costs will almost always exceed benefits.
The basic problem:
Contentious actors usually pursue public or club goods, so there’s always incentive to free ride
Moreover, contentious actors face high costs: being on the losing side of a rebellion has a huge downside.
The expectation that others will free-ride makes participation even less attractive (because \(P(PG)\) depends partly on the number of people who choose to join)
Consider a payoff structure like this:
| Actor B: Join the rebellion | Actor B: Stay home | |
|---|---|---|
| Actor A: Join the rebellion | Revolution: we both get what we want but we split the costs of joining | Revolution: (but Actor B avoids all costs) |
| Actor A: Stay home | Revolution (but actor A avoids all costs) | Mutual defection: actor A and B get nothing |
Where do rational actors end up?
The “supply” of collective action doesn’t meet the “demand”, but large-scale collective action still happens. Why?
If the benefit is large, the number of recipients is small, and the contribution to the \(P(PG|A)\) is significant, then even private actors will provide non-excludable goods (industry lobbying groups are a class case)
If a firm lacks competitors, they might not care about “non-excludability” (company towns, “Fordlandia”, Disneyworld)
Leaders can add a selective (\(S\)) incentive that you only receive by joining.
\[ EU(A) = U_{pg} \times P(PG|A) - C + S \]
\[ EU(\neg A) = U_{pg} \times P(PG|\neg A) \]
This is most likely to be effective when \(C\) is small.
Many interest groups (especially large ones that engage in conventional lobbying) provide selective incentives like discounts and coupons.
However, the costs of participation also need to be quite low.
Higher risk collective actors may require higher rewards to recruit, and this inevitably requires access to resources.
Resource-poor groups might rely mostly on intangible incentives and punishments (ideology, social sanction/reward, “fun”)
images from the Warsaw Uprising in Nazi occupied Poland
Monitoring/Sanctions can reassure actors that others won’t defect AND take away the incentive to do the same.
However, this presents its own problems: monitoring and sanctions are themselves a kind of public good.